Maximum Likelihood Analysis of Heapsort

We present a new approach for an average-cases analysis of algorithms that supports a non-uniform distribution of the inputs and is based on the maximum likelihood training of stochastic grammars. The approach is exemplified by an analysis of the average running time of heapsort. All but one step of our analysis can be automated on top of a computer-algebra system. Thus our new approach eases the effort required for an average-case analysis exceptionally allowing for the consideration of realistic input distributions with unknown distribution functions at the same time.